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arXiv · 1902.03625

Derivator Six-Functor-Formalisms -- Construction II

Fritz Hörmann
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Abstract

Starting from simple and necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for instance, for the stable homotopy categories of Morel-Voevodsky-Ayoub, and also for the classical setting of unbounded complexes of sheaves of Abelian groups on `nice' topological spaces. The formalism of derivator six-functor-formalisms elegantly encodes all isomorphisms between compositions of the six functors (and their compatibilities) and moreover it gives coherent enhancements over diagrams of correspondences. Such a formalism allows to extend six-functor-formalisms to stacks using (co)homological descent.

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Fritz Hörmann. 2019-02-10. Derivator Six-Functor-Formalisms -- Construction II. https://arxiv.org/abs/1902.03625

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